One of the components underlying the success of large-scale CNNs are pooling layers, introduced to formulate training in a hierarchical manner. Until recently, graph neural network (GNN) architectures used for tasks like classification, segmentation and generation, learn global graph representations by relying solely on node aggregations, neglecting the characteristics of local substructures. To mitigate such issues, several graph pooling layers have been introduced for hierarchical representation learning. Initial approaches, utilized variations of the Graclus clustering algorithm [1]}, [2]}, [3]} to perform pooling operations on the input node set. The first differentiable pooling layer (DiffPool) was introduced by [4]} that learns a soft assignment matrix to perform node clustering. However, the clustering assignment matrix requires quadratic storage complexity and it is not scalable to large scale graphs [5]}. To address the limitations of DiffPool several Top-K selection methods have been proposed, that select the top ranking nodes according to a learnable projection score [6]}, [5]}. In order to enrich the projection score with local graph structure, SAGPool [8]} utilized a GNN layer to assign self-attention scores to each node. Recently, [9]} introduced ASAPooling, an extension to Top-k pooling schemes that performs node aggregation to address the edge connectivity limitations of the previous methods. However, Top-k selection methods cannot generalize under different selections of k, which is important for simplification tasks, and therefore their applicability is limited to graph pooling layers for hierarchical learning.
